The equation to find the volume of a cylinder is V = pi • radius squared • height. The radius is half of the diameter. Half of 8 is 4, squared is 16. The height of the cylinder is 3. Our equation becomes: V = 3.14 • 16 • 3 V = 150.72 The volume of the cylinder is 150.72 inches. The equation to find the volume of a cone is V = pi • radius squared • height • 1/3. The height of the cone is 3, the radius squared is 18. Our equation becomes: V = 3.14 • 16 • 18 • 1/3 V = 904.32 • 1/3 V = 301.44 The volume of the cone is 301.44 inches. The relationship between the two volumes is that the volume of the cone is two times bigger than the volume of the cylinder.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches. Use π = 3.14. What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.